For each statement select the correct null hypothesis H0 and

For each statement, select the correct null hypothesis, H0, and alternative hypothesis, HA, in symbolic form.

(a) According to the Merck Veterinary Manual, the average resting heart rate for a certain type of sheep dog is 115 beats per minute (bpm). A Montana farmer notices his aging sheep dog has been acting more lethargic than usual. He believes that her heart rate is slower than normal for her breed. The farmer measured the dog\'s heart rate on 15 occasions and found a sample mean heart rate of 110.2 bpm. (Here represents the mean heart rate of the farmer\'s sheep dog over all occasions.)

A. H0:=115,   HA:<115
B. H0:x¯=115,   HA:x¯>115
C. H0:=115,   HA:>115
D. H0:x¯=110.2,   HA:x¯110.2
E. H0:=110.2,   HA:<110.2
F. H0:=115,   HA:115

(b) A certain type of hummingbird is known to have an average weight of 4.55 grams. A researcher believes that hummingbirds (of this same type) living in the Grand Canyon differ in weight from the population as a whole. The researcher finds a sample of 30 such hummingbirds from the Grand Canyon and calculates their average weight to be 3.75 grams. (Here represents the population mean weight of hummingbirds who live in the Grand Canyon.)  

A. H0:x¯=4.55,   HA:x¯<4.55
B. H0:x¯=3.75,   HA:x¯>3.75
C. H0:=4.55,   HA:4.55
D. H0:=3.75,   HA:3.75
E. H0:=4.55,   HA:<4.55
F. H0:<4.55,   HA:=4.55

(c) The mean height of all adult American males is 69 inches (5 ft 9 in). A researcher wants to prove that young American males between the ages of 18 and 21 tend to be taller than 69 inches. A random sample of 100 young American males ages 18 to 21 yielded a sample mean of 71 inches. (Here represents the population mean height of young American males.)  

A. H0:=69 ,   HA:>69
B. H0:x¯=71,   HA:x¯<71
C. H0:=71,   HA:<71
D. H0:x¯=69,   HA:x¯>69
E. H0:=69,   HA:69
F. H0:>69,   HA:<69

Solution

a)

The heart rate is slower (<) for the normal for her breed (115).

Thus, that is the Ha, so we have

OPTION A: A. H0:=115, HA:<115 [ANSWER,A]

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b)

The \"hummingbirds (of this same type) living in the Grand Canyon differ (=/=)\" from the population as a whole (4.55 g).

Thus, that is the Ha:

OPTION C. H0:=4.55, HA:4.55 [ANSWER, C]

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c)

A researcher wants to prove that young American males between the ages of 18 and 21 tend to be taller (>) than 69 inches.

Thus, that is the Ha:

OPTION A. H0:=69 , HA:>69 [ANSWER, A]